Physique statistique des systèmes complexes et nanobiotechnologie

Quantum Biology
We participate to the EU-funded STREP project "Phonon-assisted Processes for Energy Transfer and Sensing" (PAPETS). This project pioneers the emerging field of Quantum Biology in Europe and will focus on two problems. On the one side, we will investigate the functioning of light-harvesting complexes and try to elucidate how and why such complicated molecular machines appear to employ quantum coherence to achieve their stunning efficiency in harvesting sun light. PAPETS will also test a revolutionary model of olfaction, introduced in the 1990s by Luca Turin ( see his original paper), and holding great promise to unveil a formidable biological mechanism that still resists tenaciously to all theoretical explanations. The new mechanism posits that olfaction relies on inelastic electron tunneling. The main idea is that odorants would be recognized not through their shapes (lock-and-key recognition), but through their vibrational spectrum. The nose would thus act as a sort of nano-spectrometer.

To investigate the role of protein vibrations in exciton transfer, we have introduced the Quantum Network Model, where a coarse-grained description of protein dynamics is coupled to a tight-binding Hamiltonian, whose elements are explicitly modulated by the classical dynamics of the underlying protein. This mean-field model realizes the so-called Ehrenfest dynamics. Despite surface-hopping is prevented by construction in this theoretical framework, we find that our model allows one to get considerable insight into how specific vibrational modes affect exciton transport.

Allosteric communication in proteins
What are the structural and dynamical determinants of the astonishing ability of protein scaffolds to propagate mechanical perturbations from a given site to another precise, distant location ? We employ different coarse-grained models of protein dynamics to study this problem, coupled with concepts and methods from statistical physics such as complex networks tools and linear response theory.

We have discovered that proteins typically display normal modes that are strongly localized at multiple locations in the protein. We termed normal modes that possess two localization peaks bi-localized modes. We found that such modes express fold-rooted spatial correlations that effectively mediate long-range energy transfer. Interestingly, a study of several structures of G-protein-coupled receptors (GPCRs) shows that bi-localized modes typically exist in these structures, connecting pairs of residues at either end of the trans-membrane portions of the scaffolds.

Diffusion-controlled reactions in complex environments
A special kind of many-body interaction emerges when one considers diffusive flux to multiple sinks. This theoretical framework arises for example when one wants to model diffusion-limited reactions among complex macromolecules or within complex environments. The origin of these interaction is simple : sinks tend to screen flux away from each other and therefore the overall flux (i.e. the overall rate) is reduced with respect to additivity. One thus usually speaks of anti-cooperative interactions. In order to solve such problems, we apply several advanced methods for the solution of the time-dependent and stationary diffusion equation in complex, multi-connected domains. These include, re-expansion theorems and dual-series relations methods.
Recent applications of these methods include the calculation of the reaction rate constant of complex core-shell nanoreactors (collaboration with Helmholtz zentrum, Berlin), new insight into the role of receptor configuration on the cell surface in ligand-receptor binding and the study of how large-scale conformational rearrangements in antibodies modulate the binding rate of small antigens.

Macromolecular crowding
Diffusive transport is well understood in dilute environments with simple geometry. However, naturally occurring milieux where this kind of transport is important are usually rather crowded and characterized by complex and strongly confining landscapes. The first striking example of this is the cell, the primary reactor for all biochemical processes at the core of life itself. Between 30 % and 40 % of the available volume in a cell is occupied by all sort of biomolecules, cytoskeletal fibers and a wealth of subcellular organelles. Order-of-magnitude and greater changes are observed in binding rates in vivo, often featuring subtle modulations that are hard to explain. Remarkably, an interesting picture is emerging lately whereby the interior of the cell would share many properties with the liquid state of matter. We are tackling these problems from various angles, essentially studying modified diffusion equations both derived from microscopic stochastic exclusion processes and from basic concepts of the physics of liquids.

Recently, we have tackled the problem of how enzyme kinetics depend on the physico-chemical properties of the environment. To investigate this problem, we are performing enzyme kinetics experiments in the presence of artificial crowding agents, such as Ficoll (a highly branched polysaccharide), polymers such as PEG, small crowding molecules, such as glucose and mesoporous gels such as agarose. Furthermore, we are measuring the diffusion coefficient of reactants immersed in such complex media, using pulsed-field gradient NMR and Fluorescence recovery after photobleaching (FRAP). In parallel, we are running Brownian dynamics simulations with ultra-coarse grained models.

Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet, often the nature of the constraints coming from many-body interactions or reflecting a complex and confining environment are better understood and modeled at the microscopic level. In this paper we review the subtle link between microscopic exclusion processes and the mean-field equations that ensue from them in the continuum limit. We show that in an inhomogeneous medium, i.e. when jumps are controlled by site-dependent hopping rates, one can obtain three different nonlinear advection-diffusion equations in the continuum limit, suitable for describing transport in the presence of quenched disorder and external fields, depending on the particular rule embodying site inequivalence at the microscopic level. In a situation that might be termed point-like scenario, when particles are treated as point-like objects, the effect of crowding as imposed at the microscopic level manifests in the mean-field equations only if some degree of inhomogeneity is enforced into the model. Conversely, when interacting agents are assigned a finite size, under the more realistic extended crowding framework, exclusion constraints persist in the unbiased macroscopic representation.

Chemical transformations involving the diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced reactions" (DIR). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment’s geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DIRs, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory that is able to describe the environment’s "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DIR reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases.

We present a detailed theory for the total reaction rate constant of a composite core-shell nanoreactor, consisting of a central solid core surrounded by a hydrogel layer of variable thickness, where a given number of small catalytic nanoparticles are embedded at prescribed positions and are endowed with a prescribed surface reaction rate constant. Besides the precise geometry of the assembly, our theory accounts explicitly for the diffusion coefficients of the reactants in the hydrogel and in the bulk as well as for their transfer free energy jump upon entering the hydrogel shell. Moreover, we work out an approximate analytical formula for the overall rate constant, which is valid in the physically relevant range of geometrical and chemical parameters. We discuss in depth how the diffusion-controlled part of the rate depends on the essential variables, including the size of the central core. In particular, we derive some simple rules for estimating the number of nanocatalysts per nanoreactor for an efficient catalytic performance in the case of small to intermediate core sizes. Our theoretical treatment promises to provide a very useful and flexible tool for the design of superior performing nanoreactor geometries with optimized nanoparticle load.

Antibodies are large, extremely flexible molecules, whose internal dynamics is certainly key to their astounding ability to bind antigens of all sizes, from small hormones to giant viruses. In this paper, we build a shape-based coarse-grained model of IgG molecules and show that it can be used to generate 3D conformations in agreement with single-molecule Cryo-Electron Tomography data. Furthermore, we elaborate a theoretical model that can be solved exactly to compute the binding rate constant of a small antigen to an IgG in a prescribed 3D conformation. Our model shows that the antigen binding process is tightly related to the internal dynamics of the IgG. Our findings pave the way for further investigation of the subtle connection between the dynamics and the function of large, flexible multi-valent molecular machines.

In this paper we introduce a fully flexible coarse-grained model of immunoglobulin G (IgG) antibodies parametrized directly on cryo-EM data and simulate the binding dynamics of many IgGs to antigens adsorbed on a surface at increasing densities. Moreover, we work out a theoretical model that allows to explain all the features observed in the simulations. Our combined computational and theoretical framework is in excellent agreement with surface-plasmon resonance data and allows us to establish a number of important results. (i) Internal flexibility is key to maximize bivalent binding, flexible IgGs being able to explore the surface with their second arm in search for an available hapten. This is made clear by the strongly reduced ability to bind with both arms displayed by artificial IgGs designed to rigidly keep a prescribed shape. (ii) The large size of IgGs is instrumental to keep neighboring molecules at a certain distance (surface repulsion), which essentially makes antigens within reach of the second Fab always unoccupied on average. (iii) One needs to account independently for the thermodynamic and geometric factors that regulate the binding equilibrium. The key geometrical parameters, besides excluded-volume repulsion, describe the screening of free haptens by neighboring bound antibodies. We prove that the thermodynamic parameters govern the low-antigen-concentration regime, while the surface screening and repulsion only affect the binding at high hapten densities. Importantly, we prove that screening effects are concealed in relative measures, such as the fraction of bivalently bound antibodies. Overall, our model provides a valuable, accurate theoretical paradigm beyond existing frameworks to interpret experimental profiles of antibodies binding to multi-valent surfaces of different sorts in many contexts.